Balancing sub- and supra-salt strain in salt-influenced rifts:

The structural style of salt-influenced rifts may differ from those formed in predominantly brittle crust. Salt can decouple sub- and supra-salt strain, causing sub-salt faults to be geometrically decoupled from, but kinematically coupled to and responsible for, supra-salt forced folding. Salt-influenced rifts thus contain more folds than their brittle counterparts, an observation often ignored in extension estimates. Fundamental to determining whether sub- and supra-salt structures are kinematically coherent, and the relative contributions of thin- (i.e. gravity-driven) and thick-skinned (i.e. whole-plate stretching) deformation to accommodating rift-related strain, is our ability to measure extension at both structural levels. We here use published physical models of salt-influenced extension to show that line-length estimates yield more accurate values of sub- and supra-salt extension compared to fault-heave, before applying these methods to seismic data from the Halten Terrace, offshore Norway. We show that, given the abundance of ductile deformation in salt-influenced rifts, significant amounts of extension may be ignored, leading to the erroneous interpretations of thin-skinned, gravity-gliding. If a system is kinematically coherent, supra-salt structures can help predict the occurrence and kinematics of sub-salt faults that may be poorly imaged and otherwise poorly constrained.


Structural styles in salt-influenced rifts
The structural style and evolution of rifts that contain rheological heterogeneities, such as to differing structural styles or a geometric disparity, above and below the intra-stratal detachment 6 ability to determine the degree of kinematic coherence between sub-and supra-salt fault systems? 115 We use two techniques to answer these questions. First, we apply the fault-heave and line-length 116 methods for estimating sub-and supra-salt extension to scaled physical models of salt-influenced 117 extension presented by . These models simulate the sub-and supra-118 salt faulting and folding patterns, and in contrast to natural examples, the boundary conditions (e.g. 119 the true extension and supra-salt rheology) are known, allowing application and assessment of the 120 relative merits of the two methods for estimating extension in salt-influenced rifts. Second, we 121 apply the same methods for estimating extension to a 3D seismic survey from the Halten Terrace,122 offshore Norway, to determine whether the supra-salt structural style is related to thick-skinned, 123 whole-plate stretching or thin-skinned, independent, gravity-driven deformation. The Halten 124 Terrace is covered by high-quality 3D and 2D seismic reflection data, which image three-125 dimensional structural style of the sub-and supra-salt fault arrays. In addition, abundant well data, 126 tied to a regional stratigraphic framework, enables mapping of sub-and supra-salt strata to 127 constrain the timing of structural development. Given that the salt in this location is relatively thin 128 (c. 400 m) and immobile compared to other salt-influenced basins in the North Sea, diapirism is 129 minimal and no allochthonous salt bodies are developed, thereby permitting the study of salt-130 influenced rift structures without significant structural overprinting. We show that sub-and supra-131 salt structural styles can be significantly different, and that line-length analysis, which explicitly 132 considers folding as a key part of the extension-related strain, is more accurate than fault-heave 133 summation in calculating extension estimates in salt-influenced rifts. We find that, despite sub-134 and supra-salt strata being extended by similar amounts and thus being kinematically coherent, 135 supra-salt strata preferentially accommodate strain by folding, whereas sub-salt strata tend to fault. 136 Our results highlight that kinematic coherence does not necessitate similar structural styles, and  (Table 2). 152 Insert Table 2 153 The physical models consist of three layers (Fig. 4) -a metal base that represents sub-salt strata, 154 an overlying silicone gel polymer that represents the salt, and an upper layer of either homogeneous 155 dry sand or wet clay, representing the sedimentary supra-salt. Localised cataclastic faulting was 156 the primary deformation style in the dry sand models (models 7, 8 and 9); as is common in such 8 (Model 12); however, with increasing strain, deformation became more localised. During the 160 experiment (see , for a full description), a constant downward 161 movement on a 45º dipping precut surface in the metal base simulated displacement along a single 162 sub-salt fault. With increasing slip, the silicone gel (salt) and the pre-kinematic (= pre-extension) 163 supra-salt were folded and then faulted, with subsiding areas being filled with sand or clay to 164 simulate syn-extension deposition. After each experiment, the models were sliced to create a series 165 of cross sections . We then measured the amount of extension in 166 each cross section using two approaches: (i) fault-heave summation, and (ii) line-length, and then 167 compared to the known values from , to evaluate their accuracy in  (Marrett and Allmendinger, 1992;Burberry, 2015). This approach 176 allows us to compare two commonly employed approaches for estimating extension and to see 177 whether, in a kinematically coherent example (i.e. sub-salt = supra-salt extension), the extension 178 approaches used can be applied to the Halten Terrace natural example and evaluated. If an 179 additional extension episode has affected either the sub-or supra-salt strata, the measured amount 180 of extension will be greater. For example, if additional, thin-skinned gravity-driven deformation, 181 independent of whole-plate stretching has taken place, the extension will be greater in the supra-182 9 salt compared to the sub-salt (Fig. 2 -unbalanced system). In contrast, if polyphase rifting has 183 occurred, then the sub-salt extension will be larger than that of the supra-salt. 184 Insert Figure 4 185 The seismic reflection data set consists of a 3D seismic survey and a series of 2D seismic lines 186 covering c. 3,200 km 2 of the Halten Terrace, offshore Norway ( Fig. 5a-b), including the Midgard 187 and Smørbukk-Heidrun segments and the Grinda Graben (structural terminology after Koch and 188 Heum, 1995). The 3D and 2D seismic surveys are time-migrated and are zero-phase with European 189 Polarity (Brown, 2001). They have a record length of 6,000 ms. Inline and crossline spacing is were tied to the seismic data. Seismic reflection data was then depth-converted using a checkshot-195 derived time-depth relationship (Appendix C). By tying the well and seismic data, we identified 196 seven key age-constrained pre-to post-salt seismic horizons: these were mapped to establish the 197 structural style for sub-and supra-salt strata ( Fig. 6; Appendix B). We mapped >200 faults, which 198 were categorised as sub-, supra-salt restricted or through-going. The study area is divided into 199 three domains based on prominent along-strike changes in supra-salt fault strike: (i) northern heave and line-length methods, we anticipate an error of c. ± 1% for measured extension. We also 218 note, in cases where fault-related folding is significant, fault-heave summation requires projection 219 of the footwall and hangingwall cut-offs (Appendix D); this may introduce a further c. ± 1% 220 measurement error for measured extension. This issue does not apply to the line-length method as 221 no stratal projection is required (see Appendix E for further details on uncertainties and errors).  Table 3-6   230 All models had an initial length (l0) of 330 mm, hence sub-and supra-salt strata had the same 231 initial line lengths and have been deformed by similar amounts; extension at both levels should 232 therefore balance. However, applying a fault-heave summation approach to models 7 and 8 233 produces a discrepancy in apparent extension between sub-and supra-salt strata, with the sub-salt 234 experiencing greater extension than the supra-salt. In contrast, when the line-length approach is 235 used, sub-and supra-salt extension broadly balance (discrepancy of <1%). Furthermore, different 236 approaches may yield different results (Fig. 4). For example, in models 7 and 8 (Table 3-4), 237 estimates of extension using line-length analysis are <50% larger than the fault-heave summation 238 approach, and similar to the known values, suggesting that folding may accommodate up to 50% 239 of the observable strain, similar to seismic-scale estimates by . In models 240 lacking appreciable folding (Model 9;     in an intra-rift subaerial basin in an arid climate, which became isolated during a regional sea-level      7) fault blocks that are more deeply buried to the west (Fig. 10). The northern domain is dominated 295 by SE-and NW-dipping, dominantly NE-SW-striking sub-salt faults, with <1 km across-strike 296 spacing (Fig. 7b). Horst-graben structures are common, with the mean westward dip of the Top 297 Sub-salt being relatively steep (c. <7°). Fault throw ranges between 100 -300 m in the east, and 298 increases to c. 500 m in the west. Sub-salt faults do not breach the overlying salt (Fig. 10a).

299
In the central domain, sub-salt faults strike N-S to NE-SW, with <4 -6 km across-strike spacing 300 (Fig. 7b). Faults dominantly dip to the west (at c. 65°), and bound a series of fault blocks that 301 downstep to the west, with a steep regional dip (<7°). Faults throw is greatest in the east (<600 m), 302 with easternmost faults breaching the salt and supra-salt strata (Fig. 10b).

303
The southern domain is characterised by NE-SW striking normal faults, with typical across-     Imber, 2012). More specifically, in the Halten Terrace, folding may accommodate for as much as 364 half of the observable extension, a result similar to that obtained from the physical models (Table   365 3-4). In the northern and southern domains, supra-salt extension derived from line-length is 366 significantly larger (c. <12% larger) than its sub-salt counterpart, similar to the fault-heave  For a sub-and supra-salt fault-fold system to be considered kinematically coherent, total 381 extension must be balanced, and the different levels must undergo deformation synchronously 382 (Walsh and Watterson, 1991). However, it is often difficult to know when sub-salt faults were 383 active. In most cases, this is related to: (i) low-quality, regional, 2D seismic reflection data, which  our ability to determine whether sub-and supra-salt deformation is kinematically coherent.

407
Furthermore, a reliance on fault-heave summation alone in folded supra-salt strata may lead to 408 inaccurate estimates of the amount of extension and the mode of crustal extension. In this section, 409 we discuss the wider implications of our study, with specific reference to: (i) sub-and supra-salt       2. When estimating extension in physical models, we show that line-length is more accurate 503 than fault-heave summation. This is largely attributed to a failure to include ductile strain 504 (folding) in fault-heave approaches, which is very common in salt-influenced rifts.   Marine and Petroleum Geology, v. 12, no.     shown. (c) An uninterpreted and interpreted regional 2D seismic line through the Halten Terrace documenting the 3D seismic extent and regional structural style. See Figure 6 for the colours used in the seismic section. The 2D seismic line has not been used for calculating extension in Figure 7.          Figure 5, and Figure 10. The colours on the interpreted sections are shown in Figure 6. Vertical exaggeration is 2.5. These sections have been used to document the structural style and were not used to calculate extension in Figure 7.

Term Definition
Ductile strain A change in shape produced by structures which are too small to be imaged individually by a particular technique and/or too small to be represented individually on a given cross-section or map, albeit in a physical model or seismic data .
Brittle strain Discontinuities that can be imaged by a particular technique on a given cross-section or map e.g. a fault, albeit in a physical model or seismic .
Thin-skinned Deformation that is restricted to the detachment and its overburden. It is typically driven by gravity (e.g. Brun and Fort, 2011), although it may occur during stretching of the entire crust or rifting (see 'thick-skinned').
Thick-skinned Deformation involving sub-and supra-salt stratigraphy, and the salt layer itself, driven by whole-plate stretching or rifting.

Supra-salt
Rock units overlying and deformation occurring above the salt. Synonymous with the terms 'cover' and 'overburden'.
Sub-salt Rock units underlying and deformation occurring below the salt. Synonymous with 'acoustic basement'.

Kinematic coherence
The timing and rates of displacement at each point on all faults in an array are largely synchronous. Not all points on all fault surfaces will be active throughout the life of the array, but the time of fault initiation and death, and growth rate, are fixed in relation to the overall growth history of the array (Walsh and Watterson, 1991). Individual faults within the array need not be physically connected.
Geometric coherence Displacements on faults may aggregate to produce a displacement distribution resembling a single fault (Walsh and Watterson, 1991;Childs et al., 1995).
Soft-linked fault(s) Faults surfaces which, at the scale of observation, appear physically disconnected, but between which mechanical and geometrical continuity is achieved by ductile strain in the intervening rock volume (Walsh and Watterson, 1991).     Table 3 Table 6 -A comparison of measured extension using the line-length and fault-heave methods with the known values for Model 12 from . The amount of extension (e) is the difference between the final and initial length of the model (e = l 1 -l 0 ). The percentage of extension (E) is the ratio of the amount of extension to the initial length (E = e/l 0 ).

Fault-heave summation
Horizontal extension (e) was calculated for two pre-kinematic horizons, one above and one below the salt. Fault heave was measured perpendicular to the dominant fault strike, and summed to give a total fault heave along the horizon of interest between horizon cut-offs. Cutoffs were defined using an extrapolated line that follows the regional trend of the chosen horizon prior to folding (Appendix D) , removing the effect of faultparallel folding . By measuring the present-day width of the section (l 1 ), the pre-extension initial width can be calculated (l 0 = l 1 -e). The percentage of extension of the pre-extension width (E) was calculated using a ratio of total fault heave (horizontal extension, e) to the pre-extension width i.e. E = e / l 0 . This method only considers brittle deformation, and does not require a velocity model as all deformation is assumed to horizontal. However, when projecting the horizon cut-offs, velocity models will slightly affect the heave estimate. No extension-related thickness variations are assumed, and line-length is preserved during extension.
For the physical models (Appendix A) from , the Top Sub-salt and the black marker bed within the supra-salt strata were used to estimate extension. Sensitivity testing was then undertaken to investigate the measurement error associated with fault-heave summation along pre-kinematic horizons in the physical models. In all cases, we found that the measurement error was not significant (c. ± 1%), and the error associated with cut-off projection (Appendix D) was also not significant (c. ± 1%). The value of extension between pre-kinematic horizons was minimal (c. ± 1%).
For the Halten Terrace, the Top Ror Formation and Top Sub-salt horizons (Fig. 6) were used to estimate extension, and the discrepancy between the two was quantified (Fig. 7). Here, fault heave was measured was measured perpendicular to the dominant fault strike every 500 m along-strike, and summed to give a total fault heave along the horizon of interest. Similarly to the physical models, sensitivity testing was undertaken along the pre-kinematic horizons in seismic sections to investigate the uncertainty associated with measurement in section. We found that measured extension varied by c. ± 4%, and was very dependent on the projection of and final position of cut-offs (Appendix D), which is in turn dependent on the velocity model, and the complexity of faulting and folding (e.g. Judge and Allmendinger, 2011). Repeat measurements of the same horizon were undertaken to determine the measurement precision under the same velocity model etc., and varied by c. ± 2%. We also note that the value of extension changes between pre-kinematic horizons, but it was not significant (c. ± 2%).

Line-length
Horizontal extension was calculated for two pre-kinematic horizons (Fig. 6), one above and one below the salt on a series of sections. The initial, pre-extension width (l 0 ) of a unit was measured by unfolding the horizon of interest and summed to give a total, perpendicular to the fault strike every 1000 m. The present-day, post-extension width (l 1 ) was then measured along the same section. The amount of extension (e) was calculated by subtracting the pre-extension width from the final, post-extension width i.e. e = l 1 -l 0 . The percentage of extension of the pre-extension width (E) was calculated using a ratio of the total horizontal extension to the preextension width i.e. E = e / l 0 . The line-length method considers brittle (faulting) and ductile (folding) deformation when estimating the initial length. No extension-related thickness variations are assumed, and line-length is preserved during extension.
For the physical models (Appendix A) from , the Top Sub-salt and the black marker bed within the supra-salt strata was used to estimate extension (Fig. 4). Given the measurement error associated with line-length in section, we undertook sensitivity testing to assess the degree of variability of extension values. We found that the amount of extension is not significantly affected by measurement (c. ± 1%). The value of measured extension also does not typically vary between horizons (c. ± 1%).
For the Halten Terrace, the Top Ror Formation and Top Sub-salt horizons were used to estimate extension (Fig. 6), and the discrepancy between the two was quantified (Fig. 7). In this case, a velocity model (Appendix C) is required as vertical and horizontal components of deformation are considered. Sensitivity testing was undertaken using a range of sub-salt velocities (c. 3 -5 km/s), where well checkshots were not available, the percentage of extension (E) is not significantly affected (± 2%); given sub-salt strata is predominantly faulted, the effect of fold amplitude on extension is negligible. To assess the likely measurement error associated with line-lengths in the Halten Terrace seismic sections, we measured the same pre-kinematic horizon several times; we found that extension values were not significantly impacted by measurement variations (c. ± 1%). We also compared extension estimates from several suprasalt pre-kinematic horizons, and found that although extension estimates did change, linelength derived extension values did not change significantly (c. ± 2%). In addition, decompaction using shale vs. sand compaction curves (Sclater and Christie, 1980) may lead to variations of extension (c. ± 1%) as the horizon line-length changes.

Line-length vs. fault-heave errors
We found that extension estimates derived from fault-heave are less precise and less accurate compared to a line-length approach when taking into account measurement issues in both physical models and seismic. Decreased precision and accuracy associated with the fault-heave method may be largely attributed with the difficulty of projecting cut-offs (Appendix D) in areas where extension is accommodated as complex folding as well as faulting. Although beyond the scope of this study, this would be exacerbated between the same seismic data in time vs. depth given the cut-offs may be projected differently. In contrast, line-length requires no such projection (except when accounting for significant footwall erosion), and instead, assumes the line-length remains unchanged during extension. Furthermore, there are fewer opportunities for the interpreter to make errors in a line-length approach relative to fault-heave summation.
Calculated errors for estimate extension associated with each method in the physical models and the Halten Terrace, offshore Norway. If the discrepancy between all of the sub-and supra-salt faults is < 30°, then heave may have been overestimated by 16% of the calculated extension value i.e. 0.16 x extension. As the sections used to calculate extension are perpendicular to the largest, dominant fault strike, the overestimate of heave is only likely on the relatively small faults, which are unlikely to significantly affect our results, and especially compared to the cumulative errors in the prior section.

Structural restoration of the Halten Terrace
To validate our interpretation of the seismic horizons in the Halten Terrace, we undertake structural restoration, following the procedure outlined in Lingrey and Vidal-Royo (2015) and  using Midland Valley's Move software (Appendix F). We chose a line of section oriented perpendicular to the regional strike of major faults and folds, and the major transport direction. We interpreted regional horizons (Fig. 5) and assigned lithological information, based upon local well information, to each stratigraphic interval and then sequentially decompacted the supra-salt overburden using compaction curves from the North Sea (Sclater and Christie, 1980). When appropriate we restored supra-salt fault blocks using rigid body rotation, making the uppermost layers subparallel to the sub-horizontal datum. Rotation was followed by unfolding of the layers using inclined shear; the shear angle was chosen via trial and error, by finding the angle that provides the least variations in the area and layer shape. The shear inclination is typically antithetic to the fault dip, and chosen angles range between 60 and 75°, and may vary between fault blocks. When fault blocks are translated and gathered, areas of mismatch are aligned as such that the area of the gap is roughly equal to the area of overlap (after Lingrey and Vidal-Royo, 2015). These gaps will either lead to an underestimate the extension if no overlap occurs, or an overestimate if the overlap is too great. Once the basins have been translated and unfolded, the next layer is decompacted. The process is repeated until the supra-salt layers have been successively restored. Given the close vertical spacing within the relatively thin Jurassic interval (Appendix B), some horizons have been omitted from the restoration.
The movement of sub-salt faults is poorly constrained, however, the hard-linked fault joining the sub-salt and supra-salt strata is used to infer the movement of the sub-salt. By removing the throw along the hard-linked fault at the supra-salt level, the throw at the sub-salt level is also removed. To calculate the remaining position of the sub-salt faults, the sub-salt blocks undergo rigid body rotation (as with the supra-salt) and are translated. The area of the salt is maintained throughout the restoration as the salt is relatively immobile in the Halten Terrace, although in reality salt likely flows in and out of the section. Once the supra-salt units have been reconstructed to the Mid Jurassic (and the Intra Åre Fm is restored to sub-horizontal), the subsalt fault blocks are unfolded using inclined shear.
The line-length variation between the present-day and restored section is minimal (< 2%). We find that once the sub-salt is fully restored, the sub-salt line-length is very similar (~ 660m difference) to that of the supra-salt (Intra Åre Fm) i.e. sub-and supra-salt extension is balanced, indicative of kinematic coherence.
Supra-salt values for extension derived from line-length may vary dependent on decompaction in the restoration procedure described above (± 1% between shale and sand decompaction trends; Section 2.3). Decompaction also strongly influences the in-section area of the units throughout the restoration process, leading to < 60% area variations between the deformed, present-day state vs. the restored state.
A To assess the quality of our block restoration and area balance, we followed the method of Lingrey and Vidal-Royo (2015). We compared the overlaps/gaps in the restoration following rigid block translation and decompaction of the overburden, to calculate the area mismatch i.e. the ratio of the "Decompacted area" with the "Net area of the gaps/overlaps". The results are presented below: Lingrey and Vidal-Royo (2015) suggest that good restorations should have areal mismatch values below 5%; when mismatch errors exceed 5%, the balance is considered poor and either the deformed state interpretation needs modification, different unfolding parameters/techniques need to be tried, or a geologic reason for the discrepancy needs to be offered. Our values, which are typically < 2% suggest that our interpretation is valid and can be considered balanced. The overburden has been decompacted, and the fault blocks have undergone rigid body rotation and translation to near horizontal. The horizon to be restored was then unfolded to horizontal using flexural slip. When the supra-salt faults are restored, the hard-linked fault (directly connecting the sub-and supra-salt strata) was backstripped, reconstructing fault activity to the east. The remaining sub-salt fault activity is poorly constrained so a constant area for the salt is assumed, however, our analysis shows the sub-and supra-salt faults are kinematically coherent hence are active at similar times. For a full description of the structural restoration procedure, see Appendix E. The position of future faults are shown as dashed lines. Line-length was measured on the restored section versus the original interpretation (Appendix E). Colours shown in Figure 5. All sections have been depth converted using the time-depth relationship in Appendix C.